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Chapter 10
Modern Atomic Theory
Greek Idea
Democritus and
Leucippus
 Matter is made up
of indivisible
particles
 Dalton - one type
of atom for each
element

Thomson’s Model
Discovered electrons
 Atoms were made of
positive stuff
 Negative electron
floating around
 “Plum-Pudding”
model

Rutherford’s Model
Discovered dense
positive piece at
the center of the
atom
 Nucleus
 Electrons moved
around
 Mostly empty
space

Bohr’s Model
 Why
don’t the electrons fall into the
nucleus?
 Move like planets around the sun.
 In circular orbits at different levels.
 Amounts of energy separate one
level from another.
Bohr’s Model
Nucleus
Electron
Orbit
Energy Levels
Bohr’s Model
Increasing energy
Fifth
Fourth
Third
Second
First
Nucleus
Further away
from the
nucleus means
more energy.
 There is no “in
between”
energy
 Energy Levels

The Quantum Mechanical
Model
Energy is quantized. It comes in chunks.
 A quanta is the amount of energy needed to
move from one energy level to another.
 Since the energy of an atom is never “in
between” there must be a quantum leap in
energy.
 Schrodinger derived an equation that
described the energy and position of the
electrons in an atom

The Quantum Mechanical
Model
Things that are very small
behave differently from things
big enough to see.
 The quantum mechanical
model is a mathematical
solution
 It is not like anything you can
see.

The Quantum Mechanical
Model
Has energy levels for
electrons.
 Orbits are not circular.
 It can only tell us the
probability of finding
an electron a certain distance from
the nucleus.

The Quantum Mechanical
Model
The atom is found
inside a blurry
“electron cloud”
 A area where there is
a chance of finding
an electron.
 Draw a line at 90 %

Atomic Orbitals
Principal Quantum Number (n) = the
energy level of the electron.
 Within each energy level the complex
math of Schrodinger’s equation
describes several shapes.
 These are called atomic orbitals
 Regions where there is a high
probability of finding an electron.

S orbitals
1 s orbital for
every
energy
level
 Spherical
shaped
 Each s orbital can hold 2 electrons
 Called the 1s, 2s, 3s, etc.. orbitals.

P orbitals




Start at the second energy level
3 different directions
3 different shapes
Each can hold 2 electrons
P Orbitals
D orbitals
Start at the second energy level
 5 different shapes
 Each can hold 2 electrons

F orbitals
Start at the fourth energy level
 Have seven different shapes
 2 electrons per shape

F orbitals
Summary
# of
Max
shapes electrons
Starts at
energy level
s
1
2
1
p
3
6
2
d
5
10
3
f
7
14
4
By Energy Level
First Energy Level
 only s orbital
 only 2 electrons
2
 1s

Second Energy
Level
 s and p orbitals
are available
 2 in s, 6 in p
 2s22p6
 8 total electrons

By Energy Level
Third energy level
 s, p, and d
orbitals
 2 in s, 6 in p, and
10 in d
 3s23p63d10
 18 total electrons

Fourth energy
level
 s,p,d, and f
orbitals
 2 in s, 6 in p, 10
in d, ahd 14 in f
2 6 10 14
 4s 4p 4d 4f
 32 total electrons

By Energy Level
Any more than
the fourth and not
all the orbitals will
fill up.
 You simply run
out of electrons

The orbitals do
not fill up in a
neat order.
 The energy levels
overlap
 Lowest energy fill
first.

Increasing energy
7s
6s
5s
7p
6p
5p
4p
4s
3p
3s
2p
2s
1s
6d
5d
4d
3d
5f
4f
Electron Configurations
The way electrons are arranged in
atoms.
 Aufbau principle- electrons enter the
lowest energy first.
 This causes difficulties because of the
overlap of orbitals of different energies.
 Pauli Exclusion Principle- at most 2
electrons per orbital - different spins

Electron Configuration
Hund’s Rule- When electrons occupy
orbitals of equal energy they don’t
pair up until they have to .
 Let’s determine the electron
configuration for Phosporus
 Need to account for 15 electrons

Increasing energy
7s
6s
5s
7p
6p
6d
5d
5p
4d
4p
3d
4s
3p
3s
2s
1s
The first to electrons
go into the 1s orbital
2p
 Notice the opposite
spins
 only 13 more

5f
4f
Increasing energy
7s
6s
5s
7p
6p
6d
5d
5p
4d
4p
3d
4s
3p
3s
2s
1s
The next electrons
go into the 2s orbital
2p
 only 11 more

5f
4f
Increasing energy
7s
6s
5s
4s
3s
2s
1s
7p
6p
5p
4p
6d
5d
4d
3d
3p • The next electrons go
into the 2p orbital
2p
• only 5 more
5f
4f
Increasing energy
7s
6s
5s
4s
3s
2s
1s
7p
6p
5p
4p
6d
5d
4d
3d
3p • The next electrons go
into the 3s orbital
2p
• only 3 more
5f
4f
Increasing energy
7s
6s
5s
4s
7p
6p
6d
5d
5p
4d
4p
3p •
3s
2s
1s
2p •
•
•
5f
4f
3d
The last three electrons
go into the 3p orbitals.
They each go into
seperate shapes
3 upaired electrons
1s22s22p63s23p3
The easy way to remember
7s 7p 7d 7f
6s 6p 6d 6f
5s 5p 5d 5f
4s 4p 4d 4f
3s 3p 3d
2s 2p
1s
•
2
1s
• 2 electrons
Fill from the bottom up
following the arrows
7s 7p 7d 7f
6s 6p 6d 6f
5s 5p 5d 5f
4s 4p 4d 4f
3s 3p 3d
2s 2p
1s
•
2
2
1s 2s
• 4 electrons
Fill from the bottom up
following the arrows
7s 7p 7d 7f
6s 6p 6d 6f
5s 5p 5d 5f
4s 4p 4d 4f
3s 3p 3d
2s 2p
1s
•
2
2
6
2
1s 2s 2p 3s
• 12 electrons
Fill from the bottom up
following the arrows
7s 7p 7d 7f
6s 6p 6d 6f
5s 5p 5d 5f
4s 4p 4d 4f
3s 3p 3d
2s 2p
1s
•
2
2
6
2
1s 2s 2p 3s
6
2
3p 4s
• 20 electrons
Fill from the bottom up
following the arrows
7s 7p 7d 7f
6s 6p 6d 6f
5s 5p 5d 5f
4s 4p 4d 4f
3s 3p 3d
2s 2p
1s
•
2
2
6
2
1s 2s 2p 3s
6
2
10
6
3p 4s 3d 4p
5s2
• 38 electrons
Fill from the bottom up
following the arrows
7s 7p 7d 7f
6s 6p 6d 6f
5s 5p 5d 5f
4s 4p 4d 4f
3s 3p 3d
2s 2p
1s
•
2
2
6
2
1s 2s 2p 3s
6
2
10
6
3p 4s 3d 4p
5s2 4d10 5p6 6s2
• 56 electrons
Fill from the bottom up
following the arrows
7s 7p 7d 7f
6s 6p 6d 6f
5s 5p 5d 5f
4s 4p 4d 4f
3s 3p 3d
2s 2p
1s
•
2
2
6
2
1s 2s 2p 3s
6
2
10
6
3p 4s 3d 4p
5s2 4d10 5p6 6s2
4f14 5d10 6p6 7s2
• 88 electrons
Fill from the bottom up
following the arrows
7s 7p 7d 7f
6s 6p 6d 6f
5s 5p 5d 5f
4s 4p 4d 4f
3s 3p 3d
2s 2p
1s
•
2
2
6
2
1s 2s 2p 3s
6
2
10
6
3p 4s 3d 4p
5s2 4d10 5p6 6s2
4f14 5d10 6p6 7s2
5f14 6d10 7p6
• 108 electrons
Exceptions to Electron
Configuration
Orbitals fill in order
Lowest energy to higher energy.
 Adding electrons can change the
energy of the orbital.
 Half filled orbitals have a lower
energy.
 Makes them more stable.
 Changes the filling order

Write these electron
configurations
Titanium - 22 electrons
 1s22s22p63s23p64s23d2
 Vanadium - 23 electrons
1s22s22p63s23p64s23d3
 Chromium - 24 electrons
 1s22s22p63s23p64s23d4 is expected
 But this is wrong!!

Chromium is actually
1s22s22p63s23p64s13d5
 Why?
 This gives us two half filled orbitals.
 Slightly lower in energy.
 The same principal applies to copper.

Copper’s electron
configuration
Copper has 29 electrons so we
expect
 1s22s22p63s23p64s23d9
 But the actual configuration is
 1s22s22p63s23p64s13d10
 This gives one filled orbital and one
half filled orbital.
 Remember these exceptions

Light
The study of light led to the
development of the quantum
mechanical model.
 Light is a kind of electromagnetic
radiation.
 Electromagnetic radiation includes
many kinds of waves
 All move at 3.00 x 108 m/s ( c)

Parts of a wave
Crest
Wavelength
Amplitude
Orgin
Trough
Parts of Wave
Orgin - the base line of the energy.
 Crest - high point on a wave
 Trough - Low point on a wave
 Amplitude - distance from origin to crest
 Wavelength - distance from crest to
crest
 Wavelength - is abbreviated l Greek
letter lambda.

Frequency
The number of waves that pass a
given point per second.
 Units are cycles/sec or hertz (hz)
 Abbreviated n the Greek letter nu

c = ln
Frequency and wavelength
Are inversely related
 As one goes up the other goes down.
 Different frequencies of light is different
colors of light.
 There is a wide variety of frequencies
 The whole range is called a spectrum

High
Low
energy
energy
Radio Micro Infrared
Ultra- XGamma
waves waves .
violet Rays Rays
Low
High
Frequency
Frequency
Long
Short
Wavelength
Wavelength
Visible Light
Atomic Spectrum
How color tells us about atoms
Prism
White light is
made up of all the
colors of the
visible spectrum.
 Passing it through
a prism separates
it.

If the light is not white
By heating a gas
with electricity we
can get it to give
off colors.
 Passing this light
through a prism
does something
different.

Atomic Spectrum
Each element
gives off its own
characteristic
colors.
 Can be used to
identify the atom.
 How we know
what stars are
made of.

• These are called
discontinuous
spectra
• Or line spectra
• unique to each
element.
• These are
emission spectra
• The light is
emitted given off.
Light is a Particle
Energy is quantized.
 Light is energy
 Light must be quantized
 These smallest pieces of light are
called photons.
 Energy and frequency are directly
related.

Energy and frequency
E=hxn
 E is the energy of the photon
 n is the frequency
 h is Planck’s constant
 h = 6.6262 x 10 -34 Joules sec.
 joule is the metric unit of Energy

The Math in Chapter 11
Only 2 equations
 c = ln
 E = hn
 Plug and chug.

Examples
 What
is the wavelength of blue light
with a frequency of 8.3 x 1015 hz?
 What is the frequency of red light
-5
with a wavelength of 4.2 x 10 m?
 What is the energy of a photon of
each of the above?
An explanation of Atomic
Spectra
Where the electron starts
When we write electron
configurations we are writing the
lowest energy.
 The energy level and electron starts
from is called its ground state.

Changing the energy
 Let’s
look at a hydrogen atom
Changing the energy

Heat or electricity or light can move the
electron up energy levels
Changing the energy

As the electron falls back to ground
state it gives the energy back as light
Changing the energy
May fall down in steps
 Each with a different energy

Ultraviolet
Visible
Infrared
 Further they fall, more energy, higher
frequency.
 This is simplified
 the orbitals also have different energies
inside energy levels
 All the electrons can move around.
What is light
Light is a particle - it comes in chunks.
 Light is a wave- we can measure its
wave length and it behaves as a wave
 If we combine E=mc2 , c=ln, E = 1/2
mv2 and E = hn
 We can get l = h/mv
 The wavelength of a particle.

Matter is a Wave
Does not apply to large objects
 Things bigger that an atom
 A baseball has a wavelength of about
10-32 m when moving 30 m/s


An electron at the same speed has a
wavelength of 10-3 cm

Big enough to measure.
The physics of the very small
Quantum mechanics explains how
the very small behaves.
 Classic physics is what you get when
you add up the effects of millions of
packages.
 Quantum mechanics is based on
probability because

Heisenberg Uncertainty
Principle
It is impossible to know exactly the
speed and velocity of a particle.
 The better we know one, the less we
know the other.
 The act of measuring changes the
properties.




More obvious with the very
small
To measure where a electron is, we use
light.
But the light moves the electron
And hitting the electron changes the
frequency of the light.
Before
Photon
Moving
Electron
After
Photon
changes
wavelength
Electron
Changes
velocity